Why quaternion algebras have rank 4 Darij Grinberg

Why quaternion algebras have rank 4

1. The statement This brief note is devoted to a simple (and well-known) result in noncommutative algebra, which is not deep but nevertheless subtler than it appears. It concerns the so-called quaternion algebras: Definition 1.1. Let k be a commutative ring1. Let a ∈ k and b ∈ k. The quaternion algebra Ha,b is defined to be the k-algebra with generators i and j and relations i2 = a, j2 = b, ij ...

Errata to " Hyperplane Arrangements and Descent Algebras "

Hyperplane arrangements and descent algebras Franco V Saliola saliola-DesAlgLectureNotes.pdf version of 10 January 2006 Errata and addenda by Darij Grinberg I will refer to the results appearing in the article " A Hyperplane arrangements and descent algebras " by the numbers under which they appear in this article. 6. Errata • Various places (for example, §2.1): You use the notations ⊆ and ⊂ sy...

Poincaré-Birkhoff-Witt type results for inclusions of Lie algebras

On the PBW theorem for pre-Lie algebras

5. Commutation of left and right actions 97 5.1. Right g-modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.2. Opposite algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.3. Analogues of results on Lie algebra actions . . . . . . . . . . . . . . 104 5.4. A theorem connecting left and right actions . . . . . . . . . . . . . . 107 5.5. The right Guin-Ou...

Research Statement Darij Grinberg

My research belongs to the field of algebraic combinatorics, centered on (but not limited to) symmetric functions and related concepts, such as combinatorial Hopf algebras, Young tableaux and trees. These objects live at the borderlands of algebra and combinatorics, often allowing for viewpoints from both sides and transfer of knowledge from one to the other. Among my contributions to this disc...